Validity of the Bible's teachings as to morality and spirituality need not be based on material evidence. However, if you want to prove the literal truth of Bible stories such as Noah's Ark, you need material evidence for your claims if you want those claims to be any more convincing than, say, the Greek myth of Athena springing fully-grown from Zeus's brow. Without evidence, both those stories are nothing more than myths.
Supernaturalism negates the applicability of science to the investigation of the origin of life.
If you're going from the premise that life was caused a supernatural event, sure. Many do not share your premise, though.
And the other side of the double standard is that believers in naturalism should not resort to supernatural evidence for morality and ethics.
So, you're saying belief in evolution is incompatible with belief in a higher code of morality and ethics?
How can one apply material evidence to a supernatural event? This inability to prove a supernatural event with material evidence is not, however, proof that the event is a myth that did not occur.
So, you're saying belief in evolution is incompatible with belief in a higher code of morality and ethics?
No, go back and read my statement. A belief in naturalism is incompatible with belief in a code of morality and ethics. It's a naturalist basis for belief in evolution that makes evolution incompatible with belief in a higher moral code. A belief in evolution from a non-naturalist basis may or may not be incompatible with belief in a higher code of morality and ethics.